Evaluate
\frac{360}{7}\approx 51.428571429
Factor
\frac{2 ^ {3} \cdot 3 ^ {2} \cdot 5}{7} = 51\frac{3}{7} = 51.42857142857143
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\begin{array}{l}\phantom{35)}\phantom{1}\\35\overline{)1800}\\\end{array}
Use the 1^{st} digit 1 from dividend 1800
\begin{array}{l}\phantom{35)}0\phantom{2}\\35\overline{)1800}\\\end{array}
Since 1 is less than 35, use the next digit 8 from dividend 1800 and add 0 to the quotient
\begin{array}{l}\phantom{35)}0\phantom{3}\\35\overline{)1800}\\\end{array}
Use the 2^{nd} digit 8 from dividend 1800
\begin{array}{l}\phantom{35)}00\phantom{4}\\35\overline{)1800}\\\end{array}
Since 18 is less than 35, use the next digit 0 from dividend 1800 and add 0 to the quotient
\begin{array}{l}\phantom{35)}00\phantom{5}\\35\overline{)1800}\\\end{array}
Use the 3^{rd} digit 0 from dividend 1800
\begin{array}{l}\phantom{35)}005\phantom{6}\\35\overline{)1800}\\\phantom{35)}\underline{\phantom{}175\phantom{9}}\\\phantom{35)99}5\\\end{array}
Find closest multiple of 35 to 180. We see that 5 \times 35 = 175 is the nearest. Now subtract 175 from 180 to get reminder 5. Add 5 to quotient.
\begin{array}{l}\phantom{35)}005\phantom{7}\\35\overline{)1800}\\\phantom{35)}\underline{\phantom{}175\phantom{9}}\\\phantom{35)99}50\\\end{array}
Use the 4^{th} digit 0 from dividend 1800
\begin{array}{l}\phantom{35)}0051\phantom{8}\\35\overline{)1800}\\\phantom{35)}\underline{\phantom{}175\phantom{9}}\\\phantom{35)99}50\\\phantom{35)}\underline{\phantom{99}35\phantom{}}\\\phantom{35)99}15\\\end{array}
Find closest multiple of 35 to 50. We see that 1 \times 35 = 35 is the nearest. Now subtract 35 from 50 to get reminder 15. Add 1 to quotient.
\text{Quotient: }51 \text{Reminder: }15
Since 15 is less than 35, stop the division. The reminder is 15. The topmost line 0051 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 51.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}